Abstract
In relativity, there is no absolute notion of simultaneity because two clocks that are in different places can always be desynchronized by a Lorentz boost. Here, we explore the implications of this effect for the quantum theory of unstable particles. We show that when a wave function is boosted, its tails travel one to the past and the other to the future. As a consequence, in the new frame of reference, the particle is in a quantum superposition decayed nondecayed, where the property decayedness is entangled with the position. Since a particle cannot be localized in a region smaller than the Compton wavelength, there is a nonzero lower bound on this effect, which is fundamental in nature. The surprising implication is that, in a quantum world, decay probabilities can never be Lorentz invariant. We show that this insight was the missing ingredient to reconcile the seemingly conflicting views about time dilation in relativistic quantum mechanics and quantum field theory.
- Received 27 June 2022
- Accepted 10 October 2022
DOI:https://doi.org/10.1103/PhysRevA.106.042215
©2022 American Physical Society